1. Field of the Invention
The present invention relates to numerical modeling and simulation methods, and particularly to a method of modeling phase changes due to laser pulse heating that utilizes energy equations and a discretizing numerical method to model temperature variation and cavity depth in a substrate material due to laser heating.
2. Description of the Related Art
In thermodynamics, a phase transition is the transformation of a thermodynamic system from one phase to another. At phase-transition point, physical properties may undergo abrupt changes, such as changes in volume, for example. Phase transitions, such as those caused by laser heating of a substrate material, typically occur between solid and liquid phases, and between liquid and vapor phases.
First-order phase transitions are those that involve a latent heat. During such a transition, a system either absorbs or releases a fixed (and typically large) amount of energy. During this process, the temperature of the system will stay constant as heat is added. Because energy cannot be instantaneously transferred between the system and its environment, first-order transitions are associated with “mixed-phase regimes” in which some parts of the system have completed the transition and others have not. This phenomenon is familiar to anyone who has boiled a pot of water, i.e., the water does not instantly turn into gas, but forms a turbulent mixture of water and water vapor bubbles. Mixed-phase systems are difficult to study, because their dynamics are violent and hard to control. However, many important phase transitions fall in this category, including the solid/liquid/gas transitions.
The equations governing such phase transitions are complex and, in some cases, impossible to solve analytically. Numeric methods must be applied, and since numerical techniques for partial differential equations often require a large amounts of time and computing power, it is difficult to develop effective numerical techniques for the calculation of phase-change related properties.
Thus, a method of modeling phase changes due to laser pulse heating solving the aforementioned problems is desired.